Inequalities and bounds for elliptic integrals

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Abstract

Computable lower and upper bounds for the symmetric elliptic integrals and for Legendre's incomplete integral of the first kind are obtained. New bounds are sharper than those known earlier. Several inequalities involving integrals under discussion are derived.

Keywords

Symmetric elliptic integrals
Legendre's elliptic integrals
The R-hypergeometric functions
Inequalities
Convexity
Means

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